Out of all "possible" final scores (0<R<3*n) for a team, participating in N games, how many final results cannot be achieved?
See The Solution  Submitted by Ady TZIDON 
Rating: 4.0000 (1 votes) 
Not achieved (spoiler) 

(I want to say the answer is zero since if a score cannot be achieved it is not possible. But I know this isn't what you mean. I don't remember this problem from the queue or I'd have suggested a rewrite.)
The answer is 1. For N games the only unachievable score is 3N1.
Numbers of the form 3m can be (W,L,D) = (m,Nm,0)
Numbers of the form 3m+1 can be (m,Nm1,1)
Numbers of the form 3m+2 can be (m,Nm2,2) except where
there is only 1 nonwin. In that case there cannot be 2 draws.
The answer is 1. For N games the only unachievable score is 3N1.
Numbers of the form 3m can be (W,L,D) = (m,Nm,0)
Numbers of the form 3m+1 can be (m,Nm1,1)
Numbers of the form 3m+2 can be (m,Nm2,2) except where
there is only 1 nonwin. In that case there cannot be 2 draws.
Posted by Jer on 20130403 11:32:42 